Related papers: Geometric Graph-Theoretic Aspects of Quantum Stabi…
We present a decoder for nonbinary CWS quantum codes using the structure of union codes. The decoder runs in two steps: first we use a union of stabilizer codes to detect a sequence of errors, and second we build a new code, called union…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
Codeword stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and non-additive quantum codes. Standard codeword stabilized quantum codes encode quantum information into…
This paper introduces a new quantization scheme for real and complex Grassmannian sources. The proposed approach relies on a structured codebook based on a geometric construction of a collection of bent grids defined from an initial mesh on…
Operator quantum error correction is a recently developed theory that provides a generalized framework for active error correction and passive error avoiding schemes. In this paper, we describe these codes in the stabilizer formalism of…
Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…
The geometric measure, the logarithmic robustness and the relative entropy of entanglement are proved to be equal for a stabilizer quantum codeword. The entanglement upper and lower bounds are determined with the generators of code. The…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…
We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces…
Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
Codeword stabilized (CWS) codes are, in general, non-additive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical non-linear codes. For an n-qubit quantum…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…
The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the…
We present a simple protocol for certifying graph states in quantum networks using stabiliser measurements. The certification statements can easily be applied to different protocols using graph states. We see for example how it can be used…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
In this work, we develop an efficient decoding method for graph codes, a class of stabilizer quantum error-correcting codes constructed from graph states. While optimal decoding is generally NP-hard, we propose a faster decoder exploiting…